发表机构
ETH Zürich; Cheriton School of Computer Science, University of Waterloo; Johns Hopkins University（苏黎世联邦理工学院; 滑铁卢大学切里顿计算机科学学院; 约翰斯·霍普金斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明稠密随机Kikuchi矩阵在维度增长时收敛到$\Gamma$-独立半圆系统，改进谱范数界，并在双重极限下收敛到$q$-高斯系统。
AI 中文摘要
Kikuchi矩阵是一族结构化矩阵，最初被引入用于研究涉及张量和超图的问题。我们证明，随着环境维度的增长，稠密随机Kikuchi矩阵具有由$\Gamma$-独立半圆元素系统描述的极限。这刻画了它们的极限谱分布，并对其谱范数给出了改进的界，谱范数是张量PCA算法分析中的关键量。最后，我们证明，在适当的双重极限下，独立的Kikuchi矩阵收敛到$q$-高斯系统，这是非交换概率中的另一个核心对象。
英文摘要
Kikuchi matrices are a family of structured matrices that were introduced to study problems involving tensors and hypergraphs. We show that, as the ambient dimension grows, dense random Kikuchi matrices have a limit described by a system of $Γ$-independent semicircular elements. This characterizes their limiting spectral distribution and yields improved bounds on their spectral norm, a key quantity in the analysis of algorithms for Tensor PCA. Finally, we show that, in an appropriate double limit, independent Kikuchi matrices converge to the $q$-Gaussian system, another central object in noncommutative probability.
